Finite Group Databasebeta

← #14419156

Subgroups — #14419156

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65983C211yesmaximal, characteristic
2#11752432C211yesmaximal, characteristic, complemented
3D4×C3⋊#170C211yesmaximal, characteristic, complemented
4#11752416C211yesmaximal, characteristic, complemented
5C2×C4×C3⋊#170C211yesmaximal, characteristic, complemented
6#11752366C211yesmaximal, characteristic, complemented
7#11752365C211yesmaximal, characteristic, complemented
8#11752362C211yesmaximal, characteristic, complemented
9#11752360C211yesmaximal, characteristic, complemented
10#11752356C211yesmaximal, characteristic, complemented
11#11752354C211yesmaximal, characteristic, complemented
12#11752352C211yesmaximal, characteristic, complemented
13#11752351C211yesmaximal, characteristic, complemented
14#11752351C211yesmaximal, characteristic, complemented
15#11752350C211yesmaximal, characteristic, complemented
16#10617292—31nomaximal, Hall
17C2×#6762C2211yescharacteristic
18C22×C3⋊#170C2211yescharacteristic
19C22×C3⋊#170C2211yescharacteristic
20C22×C3⋊#170C2211yescharacteristic
21C2×#6758C2211yescharacteristic
22C2×D5⋊(C3⋊C8)C2211yescharacteristic
23C3×C5×#123C411yescharacteristic
24C3×#4085C411yescharacteristic
25C3×D4×Dic5C2211yescharacteristic
26C3×#4075C411yescharacteristic
27C2×C3×C4×Dic5C2211yescharacteristic
28C3×#4044C411yescharacteristic
29C3×#4038C2211yescharacteristic
30C3×#4035C411yescharacteristic
31C3×#4033C2211yescharacteristic
32C3×#4031C411yescharacteristic
33C3×#4027C2211yescharacteristic
34C3×#4027C2211yescharacteristic
35C3×#4025C411yescharacteristic
36C3×#4024C411yescharacteristic
37C3×#4023C2211yescharacteristic
38#91241C2211yescharacteristic
39#91241C2211yescharacteristic
40#91241C2211yescharacteristic
41#91241C2211yescharacteristic
42#91233C2211yescharacteristic
43#91233C2211yescharacteristic
44#91233C2211yescharacteristic
45#91233C2211yescharacteristic
46#91232C2211yescharacteristic
47#91232C2211yescharacteristic
48#91231C2211yescharacteristic
49#91231C2211yescharacteristic
50#91231C2211yescharacteristic
51#91231C2211yescharacteristic
52C4⋊(C3⋊#170)C2211yescharacteristic
53C4⋊(C3⋊#170)C2211yescharacteristic
54C4×C3⋊#170C2211yescharacteristic
55C4×C3⋊#170C2211yescharacteristic
56C4×C3⋊#170C2211yescharacteristic
57C4×C3⋊#170C2211yescharacteristic
58C4×C3⋊#170C2211yescharacteristic
59C4×C3⋊#170C2211yescharacteristic
60#83126—51nomaximal, Hall
61#65983D311yescharacteristic
62#65773—31no—
63D4×#170—31no—
64#65757—31no—
65C2×C4×#170—31no—
66#65707—31no—
67#65706—31no—
68#65703—31no—
69#65701—31no—
70#65697—31no—
71#65695—31no—
72#65693—31no—
73#65692—31no—
74#65692—31no—
75#65691—31no—
76C2×C3×C5×D4C2×C411yescharacteristic
77C22×C3×C4×C5C2×C411yescharacteristic
78C2×C3×C22⋊D5C2×C411yescharacteristic
79C2×C3×C22⋊D5C2×C411yescharacteristic
80C22×C3×Dic5C2×C411yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C2×C3×C4×D5C2311yescharacteristic
84C2×C3×Dic10C2×C411yescharacteristic
85#6762—22no—
86C2×C3⋊#170—22no—
87C2×C3⋊#170—22no—
88C2×C3⋊#170—22no—
89C2×C3⋊#170C2311yescharacteristic
90C2×C3⋊#170C2311yescharacteristic
91C2×C3⋊#170C2311yescharacteristic
92C2×C3⋊#170C2311yescharacteristic
93C2×C3⋊#170C2311yescharacteristic
94C2×C3⋊#170C2311yescharacteristic
95C2×C3⋊#170C2311yescharacteristic
96C2×C3⋊#170C2311yescharacteristic
97#6758—22no—
98D5⋊(C3⋊C8)—22no—
99C3×C5×C4⋊C4C2×C411yescharacteristic
100C3×C5×C4⋊C4C2×C411yescharacteristic
101C3×C5×C22⋊C4C2×C411yescharacteristic
102C3×C5×C22⋊C4C2×C411yescharacteristic
103C3×C5×C22⋊C4C2×C411yescharacteristic
104C3×C22⋊Dic5C2×C411yescharacteristic
105C3×C22⋊Dic5C2×C411yescharacteristic
106C3×C22⋊Dic5C2×C411yescharacteristic
107C3×#685C2×C411yescharacteristic
108C3×#685C2×C411yescharacteristic
109C3×#685C2×C411yescharacteristic
110C3×#685C2×C411yescharacteristic
111C3×C4⋊Dic5C2×C411yescharacteristic
112C3×C4⋊Dic5C2×C411yescharacteristic
113C3×#683C2×C411yescharacteristic
114C3×#683C2×C411yescharacteristic
115C3×#683C2×C411yescharacteristic
116C3×#683C2×C411yescharacteristic
117C3×#683C2×C411yescharacteristic
118C3×#683C2×C411yescharacteristic
119C3×C4×Dic5C2×C411yescharacteristic
120C3×C4×Dic5C2×C411yescharacteristic
121C3×C4×Dic5C2311yescharacteristic
122C3×C4×Dic5C2311yescharacteristic
123C3×C4×Dic5C2311yescharacteristic
124C3×C4×Dic5C2311yescharacteristic
125C3×#529—51no—
126#5024—51no—
127Q8×C3⋊C8—51no—
128#5012—51no—
129#5011—51no—
130#5011—51no—
131D4×C3⋊C8—51no—
132D4×C3⋊C8—51no—
133D4×C3⋊C8—51no—
134#5000—51no—
135#5000—51no—
136#4997—51no—
137#4997—51no—
138#4926—51no—
139C2×C4×C3⋊C8—51no—
140C2×#704—31no—
141C22×#170—31no—
142C22×#170—31no—
143C22×#170—31no—
144C2×#700—31no—
145C2×D5⋊C8—31no—
146C5×#123Dic311yescharacteristic
147#4085Dic311yescharacteristic
148D4×Dic5C2×D311yescharacteristic
149#4075Dic311yescharacteristic
150C2×C4×Dic5C2×D311yescharacteristic
151#4044Dic311yescharacteristic
152#4038C2×D311yescharacteristic
153#4035Dic311yescharacteristic
154#4033C2×D311yescharacteristic
155#4031Dic311yescharacteristic
156#4027C2×D311yescharacteristic
157#4027C2×D311yescharacteristic
158#4025Dic311yescharacteristic
159#4024Dic311yescharacteristic
160#4023C2×D311yescharacteristic
161C22⋊#170—31no—
162C22⋊#170—31no—
163C22⋊#170—31no—
164C22⋊#170—31no—
165#4004—31no—
166#4004—31no—
167#4004—31no—
168#4004—31no—
169#4003—31no—
170#4003—31no—
171#4002—31no—
172#4002—31no—
173#4002—31no—
174#4002—31no—
175C4⋊#170—31no—
176C4⋊#170—31no—
177C4×#170—31no—
178C4×#170—31no—
179C4×#170—31no—
180C4×#170—31no—
181C4×#170—31no—
182C4×#170—31no—
183#2966—151noSylow
184C23×C3×C5C22×C411yescharacteristic
185C23×C3×C5C22×C411yescharacteristic
186C22×C3×D5C22×C411yescharacteristic
187C3×C5×D4—22no—
188C2×C3×C4×C5—22no—
189C2×C3×C4×C5C22×C411yescharacteristic
190C2×C3×C4×C5C22×C411yescharacteristic
191C2×C3×C4×C5C22×C411yescharacteristic
192C2×C3×C4×C5C22×C411yescharacteristic
193C2×C3×C4×C5C22×C411yescharacteristic
194C3×C22⋊D5—22no—
195C3×C22⋊D5—22no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5C22×C411yescharacteristic
202C2×C3×Dic5C22×C411yescharacteristic
203C2×C3×Dic5C22×C411yescharacteristic
204C2×C3×Dic5C22×C411yescharacteristic
205C2×C3×Dic5C22×C411yescharacteristic
206C2×C3×Dic5C22×C411yescharacteristic
207C2×C3×Dic5C2411yescharacteristic
208C3×C4×D5—21no—
209C3×C4×D5—21no—
210C3×Dic10—22no—
211C3⋊#170—21no—
212C3⋊#170—21no—
213C3⋊#170—21no—
214C3⋊#170—21no—
215C3⋊#170—21no—
216C3⋊#170—21no—
217C3⋊#170#4112yes—
218C3⋊#170#4112yes—
219C3×#126—51no—
220C3×#126—51no—
221C3×#125—51no—
222C3×#124—51no—
223C3×#123—51no—
224C3×#123AGL(1,𝔽5)11yescharacteristic
225C3×C22⋊Q8—51no—
226C3×#121—51no—
227C3×C4×Q8—51no—
228C3×C4×D4—51no—
229C3×C4×D4—51no—
230C3×C4×D4—51no—
231C3×#117—51no—
232C3×#117—51no—
233C2×C3×C42—51no—
234C2×#208—51no—
235C2×#208—51no—
236C22×C3⋊C8—51no—
237C22×C3⋊C8—51no—
238C22×C3⋊C8—51no—
239C22×C3⋊C8—51no—
240#830—51no—
241#830—51no—
242#830—51no—
243#830—51no—
244#830—51no—
245#830—51no—
246C4⋊(C3⋊C8)—51no—
247C4⋊(C3⋊C8)—51no—
248C4⋊(C3⋊C8)—51no—
249C4⋊(C3⋊C8)—51no—
250C4⋊(C3⋊C8)—51no—
251C4⋊(C3⋊C8)—51no—
252#803—51no—
253#803—51no—
254#803—51no—
255#803—51no—
256C4×C3⋊C8—51no—
257C4×C3⋊C8—51no—
258C4×C3⋊C8—51no—
259C4×C3⋊C8—51no—
260C4×C3⋊C8—51no—
261C4×C3⋊C8—51no—
262C2×C5×D4C2×Dic311yescharacteristic
263C22×C4×C5C2×Dic311yescharacteristic
264C2×C22⋊D5C2×Dic311yescharacteristic
265C2×C22⋊D5C2×Dic311yescharacteristic
266C22×Dic5C2×Dic311yescharacteristic
267C22×Dic5C22×D311yescharacteristic
268C22×Dic5C22×D311yescharacteristic
269C2×C4×D5C22×D311yescharacteristic
270C2×Dic10C2×Dic311yescharacteristic
271#704—62no—
272C2×#170—31no—
273C2×#170—31no—
274C2×#170—31no—
275C2×#170—31no—
276C2×#170—31no—
277C2×#170—31no—
278C2×#170—31no—
279C2×#170—31no—
280C2×#170—62no—
281C2×#170—62no—
282C2×#170—62no—
283#700—62no—
284D5⋊C8—62no—
285C5×C4⋊C4C2×Dic311yescharacteristic
286C5×C4⋊C4C2×Dic311yescharacteristic
287C5×C22⋊C4C2×Dic311yescharacteristic
288C5×C22⋊C4C2×Dic311yescharacteristic
289C5×C22⋊C4C2×Dic311yescharacteristic
290C22⋊Dic5C2×Dic311yescharacteristic
291C22⋊Dic5C2×Dic311yescharacteristic
292C22⋊Dic5C2×Dic311yescharacteristic
293#685C2×Dic311yescharacteristic
294#685C2×Dic311yescharacteristic
295#685C2×Dic311yescharacteristic
296#685C2×Dic311yescharacteristic
297C4⋊Dic5C2×Dic311yescharacteristic
298C4⋊Dic5C2×Dic311yescharacteristic
299#683C2×Dic311yescharacteristic
300#683C2×Dic311yescharacteristic
301#683C2×Dic311yescharacteristic
302#683C2×Dic311yescharacteristic
303#683C2×Dic311yescharacteristic
304#683C2×Dic311yescharacteristic
305C4×Dic5C2×Dic311yescharacteristic
306C4×Dic5C2×Dic311yescharacteristic
307C4×Dic5C22×D311yescharacteristic
308C4×Dic5C22×D311yescharacteristic
309C4×Dic5C22×D311yescharacteristic
310C4×Dic5C22×D311yescharacteristic
311#529—51no—
312#446—151no—
313C8×Q8—151no—
314#436—151no—
315#435—151no—
316#435—151no—
317C8×D4—151no—
318C8×D4—151no—
319C8×D4—151no—
320#433—151no—
321#433—151no—
322#432—151no—
323#405—151no—
324#405—151no—
325C2×C4×C8—151no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5—21no—
329C22×C3×C5—21no—
330C22×C3×C5—21no—
331C22×C3×C5#13112yes—
332C22×C3×C5C23×C411yescharacteristic
333C2×C3×D5—21no—
334C2×C3×D5—21no—
335C2×C3×D5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—21no—
338C3×C4×C5—21no—
339C3×C4×C5—21no—
340C3×C4×C5—21no—
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—21no—
344C3×Dic5—21no—
345C3×Dic5—21no—
346C3×Dic5#13112yes—
347C3×Dic5C2×#4111yescharacteristic
348C3×Dic5C2×#4111yescharacteristic
349C2×C3×Q8—51no—
350C2×C3×D4—51no—
351C2×C3×D4—51no—
352C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
353C22×C3×C4—51no—
354C22×C3×C4—51no—
355C22×C3×C4—51no—
356C22×C3×C4—51no—
357C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—51no—
362C3×C4⋊C4—51no—
363C3×C4⋊C4—51no—
364C3×C4⋊C4—51no—
365C3×C4⋊C4—51no—
366C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
367C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
368C3×C22⋊C4—51no—
369C3×C22⋊C4—51no—
370C3×C22⋊C4—51no—
371C3×C22⋊C4—51no—
372C3×C22⋊C4—51no—
373C3×C22⋊C4—51no—
374C3×C22⋊C4—51no—
375C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
376C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
377C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
378C3×C42—51no—
379C3×C42—51no—
380C3×C42—51no—
381C3×C42—51no—
382C3×C42—51no—
383C3×C42—51no—
384#208—102no—
385#208—102no—
386C2×C3⋊C8—51no—
387C2×C3⋊C8—51no—
388C2×C3⋊C8—51no—
389C2×C3⋊C8—51no—
390C2×C3⋊C8—51no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8—51no—
394C2×C3⋊C8—102no—
395C2×C3⋊C8—102no—
396C2×C3⋊C8—102no—
397C2×C3⋊C8—102no—
398C23×C5C22×Dic311yescharacteristic
399C23×C5C22×Dic311yescharacteristic
400C22×D5C22×Dic311yescharacteristic
401C5×D4—22no—
402C2×C4×C5—22no—
403C2×C4×C5C22×Dic311yescharacteristic
404C2×C4×C5C22×Dic311yescharacteristic
405C2×C4×C5C22×Dic311yescharacteristic
406C2×C4×C5C22×Dic311yescharacteristic
407C2×C4×C5C22×Dic311yescharacteristic
408C22⋊D5—22no—
409C22⋊D5—22no—
410C2×Dic5—22no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5C22×Dic311yescharacteristic
416C2×Dic5C22×Dic311yescharacteristic
417C2×Dic5C22×Dic311yescharacteristic
418C2×Dic5C22×Dic311yescharacteristic
419C2×Dic5C22×Dic311yescharacteristic
420C2×Dic5C22×Dic311yescharacteristic
421C2×Dic5C23×D311yescharacteristic
422C4×D5—21no—
423C4×D5—21no—
424Dic10—22no—
425#170—32no—
426#170—32no—
427#170—61no—
428#170—61no—
429#170—61no—
430#170—61no—
431#170—61no—
432#170—61no—
433C2×M16—151no—
434C2×M16—151no—
435C22×C8—151no—
436C22×C8—151no—
437C22×C8—151no—
438C22×C8—151no—
439#126—51no—
440#126—51no—
441#125—51no—
442#124—51no—
443#123—51no—
444#123ΓL(1,𝔽16)11yescharacteristic
445C22⋊Q8—51no—
446#121—51no—
447C4×Q8—51no—
448C4×D4—51no—
449C4×D4—51no—
450C4×D4—51no—
451#117—51no—
452#117—51no—
453C2×C42—51no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456C4⋊C8—151no—
457C4⋊C8—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460C22⋊C8—151no—
461C22⋊C8—151no—
462C22⋊C8—151no—
463C22⋊C8—151no—
464C22⋊C8—151no—
465C22⋊C8—151no—
466#97—151no—
467#97—151no—
468#97—151no—
469#97—151no—
470C4×C8—151no—
471C4×C8—151no—
472C4×C8—151no—
473C4×C8—151no—
474C4×C8—151no—
475C4×C8—151no—
476C2×C3×C5—22no—
477C2×C3×C5—41no—
478C2×C3×C5C4×#4111yescharacteristic
479C2×C3×C5C2×#13111yescharacteristic
480C2×C3×C5C2×#13111yescharacteristic
481C3×D5—41no—
482C23×C3—51no—
483C23×C3C22×AGL(1,𝔽5)11yescharacteristic
484C23×C3C22×AGL(1,𝔽5)11yescharacteristic
485C3×Q8—102no—
486C3×D4—22no—
487C3×D4—102no—
488C3×D4—102no—
489C2×C3×C4—22no—
490C2×C3×C4—51no—
491C2×C3×C4—51no—
492C2×C3×C4—51no—
493C2×C3×C4—51no—
494C2×C3×C4—51no—
495C2×C3×C4—51no—
496C2×C3×C4—51no—
497C2×C3×C4—101no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—102no—
504C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
505C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
506C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
507C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
508C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
509C3⋊C8—52no—
510C3⋊C8—52no—
511C3⋊C8—101no—
512C3⋊C8—101no—
513C3⋊C8—101no—
514C3⋊C8—101no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5—21no—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—21no—
521C22×C5—21no—
522C22×C5#94812yes—
523C22×C5C23×Dic311yescharacteristic
524C2×D5—21no—
525C2×D5—21no—
526C2×D5—21no—
527C4×C5—21no—
528C4×C5—21no—
529C4×C5—21no—
530C4×C5—21no—
531C4×C5—21no—
532Dic5—21no—
533Dic5—21no—
534Dic5—21no—
535Dic5—21no—
536Dic5—21no—
537Dic5#94812yes—
538Dic5D3×#4111yescharacteristic
539Dic5D3×#4111yescharacteristic
540C2×Q8—51no—
541C2×D4—51no—
542C2×D4—51no—
543C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
549M16—302no—
550M16—302no—
551C2×C8—151no—
552C2×C8—151no—
553C2×C8—151no—
554C2×C8—151no—
555C2×C8—151no—
556C2×C8—151no—
557C2×C8—151no—
558C2×C8—151no—
559C2×C8—302no—
560C2×C8—302no—
561C2×C8—302no—
562C2×C8—302no—
563C4⋊C4—51no—
564C4⋊C4—51no—
565C4⋊C4—51no—
566C4⋊C4—51no—
567C4⋊C4—51no—
568C4⋊C4—51no—
569C4⋊C4—51no—
570C4⋊C4—51no—
571C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
572C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
573C22⋊C4—51no—
574C22⋊C4—51no—
575C22⋊C4—51no—
576C22⋊C4—51no—
577C22⋊C4—51no—
578C22⋊C4—51no—
579C22⋊C4—51no—
580C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
581C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
582C22⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
583C42—51no—
584C42—51no—
585C42—51no—
586C42—51no—
587C42—51no—
588C42—51no—
589C3×C5#296611yescharacteristic, complemented, Hall
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—101no—
596C22×C3—101no—
597C22×C3—101no—
598C22×C3#413112yes—
599C22×C3C23×AGL(1,𝔽5)11yescharacteristic
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—52no—
606C3×C4—51no—
607C3×C4—51no—
608C3×C4—101no—
609C3×C4—101no—
610C3×C4—101no—
611C3×C4—101no—
612C3×C4—101no—
613C2×C5—22no—
614C2×C5—41no—
615C2×C5C2×#94811yescharacteristic
616C2×C5C2×#94811yescharacteristic
617C2×C5Dic3×#4111yescharacteristic
618D5—41no—
619C23—51no—
620C23C22×ΓL(1,𝔽16)11yescharacteristic
621C23C22×ΓL(1,𝔽16)11yescharacteristic
622Q8—102no—
623D4—22no—
624D4—102no—
625D4—102no—
626C2×C4—22no—
627C2×C4—51no—
628C2×C4—51no—
629C2×C4—51no—
630C2×C4—51no—
631C2×C4—51no—
632C2×C4—51no—
633C2×C4—51no—
634C2×C4—101no—
635C2×C4—101no—
636C2×C4—101no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—101no—
640C2×C4—102no—
641C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
642C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
643C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
644C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
645C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
646C8—152no—
647C8—152no—
648C8—301no—
649C8—301no—
650C8—301no—
651C8—301no—
652C8—301no—
653C8—301no—
654C2×C3—22no—
655C2×C3—41no—
656C2×C3—201no—
657C2×C3C2×#413111yescharacteristic
658C2×C3D5⋊#13111yescharacteristic
659C2×C3#41×AGL(1,𝔽5)11yescharacteristic
660C5#8312611yescharacteristic, complemented, Sylow
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—101no—
667C22—101no—
668C22—101no—
669C22#9199012yes—
670C22C23×ΓL(1,𝔽16)11yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—52no—
677C4—51no—
678C4—51no—
679C4—101no—
680C4—101no—
681C4—101no—
682C4—101no—
683C4—101no—
684C3#1061729211yescharacteristic, complemented, Sylow
685C2—22no—
686C2—41no—
687C2—201no—
688C2C2×#9199011yescharacteristic
689C2D5⋊#94811yescharacteristic
690C2#41×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#123C4
prime radicalC3×#4085C4
cosocleC2×C3×Dic5C24
hypercenter#123ΓL(1,𝔽16)
hypocenterC3×C5#2966
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11752432C2semidirect
3. D4×C3⋊#170C2semidirect
4. #11752416C2semidirect
5. C2×C4×C3⋊#170C2semidirect
6. #11752366C2semidirect
7. #11752365C2semidirect
8. #11752362C2semidirect
9. #11752360C2semidirect
10. #11752356C2semidirect
11. #11752354C2semidirect
12. #11752352C2semidirect
13. #11752351C2semidirect
14. #11752351C2semidirect
15. #11752350C2semidirect
589. C3×C5#2966semidirect
660. C5#83126semidirect
684. C3#10617292semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#659832
#117524322
D4×C3⋊#1702
#117524162
C2×C4×C3⋊#1702
#117523662
#117523652
#117523622
#117523602
#117523562
#117523542
#117523522
#117523512
#117523502
#106172923
#831265